A lunar gradiometer mission involves the mounting of a gradiometer on a satellite which is in a low, polar, and circular lunar orbit. The results of a numerical simulation of the mission is presented. It is shown that if the satellite is in a 50 km orbit, 1 deg and 2 deg gravity anomalies may be estimated with accuracies of 12 mgal and 1 mgal respectively. At a 100 km altitude, 2 deg gravity anomalies can be estimated with an accuracy of 12 mgal. These results assume a rotating type gradiometer with a .1E accuracy. The results can be readily scaled to reflect another level.